CONCEPT PREVIEW Find the measure of each central angle (in radians).

Key Concepts

Central Angle

A central angle is an angle whose vertex is at the center of a circle and whose sides (rays) extend to the circumference. The measure of a central angle is directly related to the arc length it subtends on the circle. Understanding central angles is crucial for solving problems involving circular motion and geometry.

Radians

Radians are a unit of angular measure used in mathematics, particularly in trigonometry. One radian is defined as the angle formed when the arc length is equal to the radius of the circle. This unit is essential for converting between degrees and radians and is commonly used in calculus and physics for its natural relationship with circular motion.

Arc Length

Arc length is the distance along the curved line of a circle between two points. It can be calculated using the formula: arc length = radius × central angle (in radians). Understanding arc length is important for determining the relationship between angles and distances in circular geometry, which is often required in trigonometric problems.